WASHINGTON — The Supreme Court is taking up a challenge to a University of Texas program that considers race in some college admissions. The case could produce new limits on affirmative action at universities, or roll it back entirely.

Abigail Fisher, the white Texan who sued the university, arrived at the high court Wednesday morning to hear the argument.

Hundreds of people also wanting seats in the courtroom waited in line on the court plaza on a gorgeous fall morning. The Rev. Jesse Jackson, a supporter of affirmative action, was among advocates on both sides of the issue who gathered outside the court.

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While quieter than other protesters who have converged on the court for big cases, several people held signs proclaiming their support or opposition to affirmative action. One man held an “End Affirmative Action Now,” while another women held a “Diversity (equals) Success” sign.

The university says the program that fills roughly a quarter of its incoming classes uses race among many factors and argues that it is necessary to provide the kind of diverse educational experience the high court has previously endorsed. The rest of its slots go to students who are admitted based on their class rank, without regard to race.

Opponents of the program say the university is practicing illegal discrimination by considering race at all.

Justice Elena Kagan is not taking part, probably because she worked on the case at the Justice Department.